Quantum Information Science and Its Contributions to Mathematics
About this Volume
Edited by: Samuel J. Lomonaco Jr., University of Maryland Baltimore County, Baltimore, MD
2010: Volume: 68
ISBNs: 978-0-8218-4828-9 (print); 978-0-8218-9284-8 (online)
This volume is based on lectures delivered at the 2009 AMS Short Course on Quantum Computation and Quantum Information, held January 3–4, 2009, in Washington, D.C.
Part I of this volume consists of two papers giving introductory surveys of many of the important topics in the newly emerging field of quantum computation and quantum information, i.e., quantum information science (QIS). The first paper discusses many of the fundamental concepts in QIS and ends with the curious and counter-intuitive phenomenon of entanglement concentration. The second gives an introductory survey of quantum error correction and fault tolerance, QIS's first line of defense against quantum decoherence.
Part II consists of four papers illustrating how QIS research is currently contributing to the development of new research directions in mathematics. The first paper illustrates how differential geometry can be a fundamental research tool for the development of compilers for quantum computers. The second paper gives a survey of many of the connections between quantum topology and quantum computation. The last two papers give an overview of the new and emerging field of quantum knot theory, an interdisciplinary research field connecting quantum computation and knot theory. These two papers illustrate surprising connections with a number of other fields of mathematics.
In the appendix, an introductory survey article is also provided for those readers unfamiliar with quantum mechanics.
Graduate students and research mathematicians interested in quantum information theory and its relations to new research areas in mathematics.
Table of Contents
Quantum information science
- Patrick Hayden – Concentration of measure effects in quantum information
- Daniel Gottesman – An introduction to quantum error correction and fault-tolerant quantum computation
Contributions to mathematics
- Howard E. Brandt – Riemannian geometry of quantum computation
- Louis H. Kauffman and Samuel J. Lomonaco, Jr. – Topological quantum information theory
- Samuel J. Lomonaco and Louis H. Kauffman – Quantum knots and mosaics
- Samuel J. Lomonaco and Louis H. Kauffman – Quantum knots and lattices, or a blueprint for quantum systems that do rope tricks
- Samuel J. Lomonaco, Jr. – A Rosetta stone for quantum mechanics with an introduction to quantum computation